We report long-duration real-time observations of the dynamics of hexagonal (rodlike) directional-solidification patterns in bulk samples of a transparent eutectic alloy. A slight forward curvature of the isotherms induces a slow dilatation of the growth pattern at constant solidification rate and triggers the rod-splitting instability. At long times, the rod-splitting frequency exactly balances the dilatation driven by the curved isotherms. The growth pattern is then disordered and nonstationary but has a sharply selected mean spacing. Well-ordered growth patterns can be grown using time-dependent solidification rates.